Here is a solution using DataFrames.jl:
julia> using DataFrames, Statistics
julia> df = DataFrame(a1 = [1,1,3,4,6,6], a2 = [1,2,3,4,5,6]);
julia> combine(groupby(df, :a1), :a2 => mean)
4×2 DataFrame
Row │ a1 a2_mean
│ Int64 Float64
─────┼────────────────
1 │ 1 1.5
2 │ 3 3.0
3 │ 4 4.0
4 │ 6 5.5
EDIT:
Here are the timings (as usual in Julia you need to remember that the first time you run some function it has to be compiled which takes time):
julia> using DataFrames, Statistics
(@v1.6) pkg> st DataFrames # I am using main branch, as it should be released this week
Status `D:\.julia\environments\v1.6\Project.toml`
[a93c6f00] DataFrames v0.22.7 `https://github.com/JuliaData/DataFrames.jl.git#main`
julia> df = DataFrame(a1=rand(1:1000, 10^8), a2=rand(10^8)); # 10^8 rows in 1000 random groups
julia> @time combine(groupby(df, :a1), :a2 => mean); # first run includes compilation time
3.781717 seconds (6.76 M allocations: 1.151 GiB, 6.73% gc time, 84.20% compilation time)
julia> @time combine(groupby(df, :a1), :a2 => mean); # second run is just execution time
0.442082 seconds (294 allocations: 762.990 MiB)
Note that e.g. data.table (if this is your reference) on similar data is noticeably slower:
> library(data.table) # using 4 threads
> df = data.table(a1 = sample(1:1000, 10^8, replace=T), a2 = runif(10^8));
> system.time(df[, .(mean(a2)), by = a1])
user system elapsed
4.72 1.20 2.00